1. ## Stoke's Theorem

I'm having a difficult time figuring this problem out and I feel like I'm missing something obvious. My professor started the problem off by separating it into 3 integrals for the 3 sides of the region and labeled them c1, c2, and c3.

I'm looking for help with parameterization and the boundaries. Any help is appreciated. Thanks!

2. Originally Posted by maxreality
I'm having a difficult time figuring this problem out and I feel like I'm missing something obvious. My professor started the problem off by separating it into 3 integrals for the 3 sides of the region and labeled them c1, c2, and c3.

I'm looking for help with parameterization and the boundaries. Any help is appreciated. Thanks!
First remember that Stokes' theorem states that

$\displaystyle \iint_{S}\curl \vec{F} \cdot \vec{n} dS=\oint_{\partial S}\vec{F}\cdot d\vec{r}$

Now we just need to parametrize the boundary in a counter clockwise direction when viewed from above

$r_1(t)=(1-t)\vec{i}+t\vec{j}$
$r_2(t)=(1-t)\vec{j}+t\vec{k}$
$r_3(t)=(1-t)\vec{k}+t\vec{i}$

Now you just need to evaluate these three line integrals